This invention relates to a method and a device for determining the number of layers of a two-dimensional atomic layer thin film, and more particularly, to a method of determining the number of layers of a two-dimensional atomic layer thin film which is applicable to the next generation of electronics, optoelectronics, and spintronics because of exceptional electronic properties and optical characteristics and excellent mechanical characteristics and chemical characteristics.
In recent years, a material limit and a physical limit of silicon have been pointed out in the semiconductor industry. Therefore, a new semiconductor material substituting for silicon and an element structure based on a new concept are demanded.
Two-dimensional atomic layer thin films having an extremely small thickness, in particular, graphene is a new semiconductor material having a high potential to respond to the above-mentioned demand. By using excellent physical properties thereof, there is a possibility of realizing a new element which overwhelms the performance of existing elements.
The two-dimensional atomic layer thin film denotes crystal in which atoms are stably arranged on a two-dimensional plane and crystal formed by laminating the above-mentioned crystal to a thickness in the order of nanometer.
As a representative two-dimensional atomic layer thin film, graphene is first given. Graphene is a single layer extracted from graphite which is a layered material consisting of sp2-hybridized carbon alone and is an extremely stable monoatomic layer planar material.
Graphene has the structure of a honeycomb-like quasi-two-dimensional sheet in which six-carbon rings, each having a regular hexagonal shape having carbon atoms at vertices, are arranged without any gap. A distance between carbon atoms is about 1.42 angstroms (1.42×10−10 m), and a layer thickness is 3.3 to 3.4 angstroms (3.3 to 3.4×10−10 m) in the case where an underlayer is graphite and is about 10 angstroms (10×10−10 m) on other substrates.
As the size of the graphene plane, various sizes varying from a molecular size with a length of one side in the order of nanometer to theoretically an infinite size can be supposed. In general, graphene denotes a single layer of graphite. However, graphene often has two or more layers as the number of layers. In such a case, graphene having one layer, two layers, and three layers are respectively referred to as monolayer graphene, bilayer graphene, and trilayer graphene. Graphene having the number of layers up to about 10 is collectively referred to as few-layer graphene. Moreover, graphene other than the monolayer graphene is referred to as multilayer graphene.
As described in “The electronic properties of graphene and carbon nanotubus” by Ando, NPG asia materials 1(1), 2009, pp. 17 to 21 (Non Patent Literature 1), an electronic state of graphene can be expressed by the Dirac equation in a low-energy region. This point contrasts strongly with an electronic state of substances other than graphene which can be well expressed by the Schrodinger equation.
An electron energy of graphene has a linear dispersion relationship with respect to a wavenumber in the vicinity of a K point, more specifically, can be expressed by two straight lines respectively having positive and negative gradients corresponding to a conduction band and a valence band. A point of intersection of the straight lines is referred to as the Dirac point at which graphene electrons have peculiar electronic physical properties of behaving as fermion having an effective mass equal to zero. Because of the above-mentioned electronic properties, graphene has a feature of exhibiting the highest mobility of 106 cm2V−1s−1 or higher among existing materials and a small temperature dependence.
The monolayer graphene is basically a metal or a semi-metal having zero band gap. When the size is in the order of nanometer, however, the band gap becomes greater. As a result, the monolayer graphene becomes a semiconductor having a finite band gap depending on a width and an edge structure of graphene. Moreover, the bilayer graphene has zero band gap without perturbation. However, when perturbation which destroys the minor symmetry between the two graphene layers, for example, an electric field is applied, the bilayer graphene has a finite gap in accordance with the magnitude of the electric field.
For example, with the electric field at 3 Vnm−1, a gap becomes about 0.25 eV. In the case of the trilayer graphene, semi-metallic electronic properties, in which the conduction band and the valence band overlap each other over a width of about 30 meV, are exhibited. In terms of the overlap of the conduction band and the valence band, the trilayer graphite is close to bulk graphite. The graphite having four or more layers also exhibits the semi-metallic electronic properties. With an increase in the number of layers, the electronic properties of graphene gradually become closer to those of bulk graphite.
Moreover, graphene is also excellent in mechanical characteristics. One layer of graphene has a remarkably large Young's modulus as large as 2 TPa (terapascal). A tensile strength is at the highest level among the existing materials.
In addition, graphene has a unique optical characteristic. For example, in a wide electromagnetic-wave region ranging from a ultraviolet region (wavelength: up to 200 nm) to a region in the vicinity of terahertz light (wavelength: up to 300 μm), a transmissivity of graphene is 1−nα (n: number of layers of graphene, n=about 1 to 10, α: fine-structure constant, α=e2/2hcε0=0.0229253012, e: elementary charge, h: Planck's constant, ε0: permittivity of vacuum), specifically, is represented not by a material constant of graphene but only by fundamental physical constants. This is a characteristic unique to graphene, which cannot be seen for other substances and materials.
Further, the transmissivity and a reflectance of graphene exhibit carrier-density dependence in the terahertz light region. This fact means that the optical characteristics of graphene can be controlled based on a field effect. It is known that other two-dimensional atomic layer thin films also have peculiar physical properties based on dimensionality.
As described above, because of the exceptional electronic properties and optical characteristics and excellent mechanical characteristics and chemical characteristics, graphene is expected to be used in a wide range of industrial field from chemicals to electronics. In particular, the use of graphene for semiconductor devices and micromechanical devices in the fields of electronics, spintronics, optoelectronics, micro/nanomechanics, and bioelectronics of the next generation has been expanded around the world. Similarly to graphene, other two-dimensional atomic layer thin films are also actively studied and developed for industrial use.
In the industrial use of the two-dimensional atomic layer thin films, a method of determining the number of layers is extremely important. This is because the electronic properties and optical characteristics of graphene remarkably change depending on the number of layers. Therefore, for the demonstration of a desired function, a device is required to be manufactured after the number of layers of graphene is previously determined.
Currently, as a method of determining the number of layers of graphene, the following three types of methods are known. That is, there are known a method employing an optical microscope described in P. Blake et al., “Making graphene visible”, Applied Physics Letters, vol 91, 2007, 063124-1-3 (Non Patent Literature 2), a method employing a surface-probe microscope such as an atomic force microscope (AFM) and a scanning tunneling microscope (STM) described in H. Hiura, T. W. Ebbesen, J. Fujita, K. Tanigaki and T. Takada, “Role of sp3 defect structures in graphite and carbon nanotubes”, Letters to nature, January 1994, vol 367, p. 148-151 (Non Patent Literature 3) and Thomas W. Ebbesen and Hidefumi Hiura, “Graphene in 3-Dimensions: Towards Graphite Origami”, Advanced Materials, vol 7, No 6, 1995, p. 582-586 (Non Patent Literature 4), and a method employing Raman spectrum described in A. C. Ferrai et al., “Raman Spectrum of Graphene and Graphene layers”, Physical Review Letters, vol 97, 2006, p. 187401-1-4 (Non Patent Literature 5).
The method of determining the number of layers of graphene using the optical microscope is based on the principle that, in graphene present on a silicon (Si) substrate covered with silicon oxide (SiO2), there occurs of a change (about 1.5% or larger) visually verifiable by the naked eye in contrast between an SiO2 surface and graphene due to a shift of an interference effect of optically reflected light at an SiO2/Si interface and the SiO2 surface in accordance with the number of layers of graphene. In this case, a thickness of the SiO2 film is limited to 90 nm or 300 nm at which the interference effect between incident light and the reflected light from the Si interface is present. A procedure of the above-mentioned method is as follows. First, graphene is applied onto the SiO2/Si substrate by an appropriate method. Next, an optical-microscope image of graphene is obtained. Finally, a contrast ratio of the SiO2 surface and that of the optical-microscope image of graphene are compared. For example, a gradation of the SiO2 surface is normalized and is regarded as 100%. Then, when a thickness of an oxide film is 90 nm, the normalized gradation of the graphene portion is reduced by about 6.45% as the number of layers increases one by one. When the thickness of the oxide film is 300 nm, the amount of reduction slightly increases. For example, the gradation is reduced to about 93.55% for the monolayer graphene, about 87.10% for the bilayer graphene, about 80.65% for the trilayer graphene, about 74.20% for four-layer graphene, about 67.75% for five-layer graphene, and about 61.30% for six-layer graphene. In this manner, the number of layers can be optically determined up to about six layers.
With the method using the surface-probe microscope, an absolute distance in a height direction of graphene applied onto an appropriate substrate is measured with a high spatial resolution of the AFM. When n is the number of layers, a thickness t of graphene measured by the AFM is expressed by: t=t0+0.34×(n−1) [nm]. Although t0 corresponds to the thickness of monolayer graphite, t0 is a constant different for each type of substrate. For example, when the substrate is made of SiO2, t0≈1 [nm]. The method of determining the number of layers with the STM is almost the same as that with the AFM. In the case with the STM, however, the substrate, on which graphene is placed, is limited to a conductive one.
In the determination of the number of layers with the Raman spectrum, the number of layers of graphene is determined based on a relative intensity ratio of a G band and a 2D band (also referred to as “G′ band”) of graphene, a wavenumber (energy) of the 2D band, and a shape of the 2D band.